1 {fa,pb}@di.fct.unl.pt Departamento de Informática, Universidade Nova de Lisboa 2825-114 Caparica — Portugal Abstract. In this paper we present some applications of a set constraint solver, Cardinal, that extends constraint solving to set variables with attached set functions and with special inferences over them. In particular, diagnosis of digital circuits and set covering problems are addre...

The Capacitated Arc Routing Problem (CARP) is a well-known and fundamental vehicle routing problem. A promising exact solution approach to the CARP is to model it as a set covering problem and solve it via branch-cut-and-price. The bottleneck in this approach is the pricing (column generation) routine. In this paper, we note that most CARP instances arising in practical applications are defined...

We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for ...

There are many different kinds of cutting stock problems (CSPs) occurring in practice and in theory having in common that they ask for a set of patterns, where each pattern is a collection of elements, to satisfy given element demands while minimizing the costs of the patterns. The classical CSP only considers fixed costs for each individual pattern, but in many practical applications an additi...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

We propose a new branch-and-bound algorithm to solve hard instances of set covering problems arising from Steiner triple systems.